I added Z-order curve to a ray tracer many years ago. Rather than using nested loops over X and Y pixel coordinates I used a single loop and de-interleaved the

I added Z-order curve to a ray tracer many years ago. Rather than using nested loops over X and Y pixel coordinates I used a single loop and de-interleaved the count to get X and Y. My thought was that this would increase the cache hit rate due to the locality of the pixels. It worked and the speedup was on the order of 10 percent. Because images are rarely power of 2 or even the same in both dimensions I opted to make a list of 32x32 blocks and rendered the blocks in Z-order as well as the pixels within (which still helped vs just tiling). Locality is a good thing to exploit.